Some centrality measures can be interpreted in terms of walks.
- Degree centrality relates to a walk of length one: The more walks of length one reach a node, the higher this centrality measure.
- Betweenness centrality relates to walks along the shortest paths. The higher the number of shortest paths that pass through a node, the higher this centrality measure.
- Eigenvector centrality relates to a walk of infinite length according to the Wikipedia entry about centrality measures.
I find this characterization of these centrality measures quite useful but I have difficulties developing an intuition why eigenvector centrality relates to walk of infinite length. Any idea?